Apparatus for creating centripetal force differential

ABSTRACT

A system for producing a relative centripetal force differential includes a turntable having a plurality of telescoping spoke elements arranged along radial lines around the center of the turntable. Each of the spoke elements has a fixed end attached to the turntable and a moveable free end opposite the fixed end. As the turntable is rotated the free end of each spoke elements is moved such that it is at a minimum distance through a minimum distance region, at a maximum distance through a maximum distance region that is opposite the minimum distance region, and increased or decreased through transition regions on either side of the minimum and maximum distance regions.

FIELD OF THE INVENTION

The present invention relates generally to machine systems for creatinga centripetal force differential, and more particularly to a rotatingsystem that uses a combination of permanent and electromagnets to opposethe outward force of magnetic masses being rotated around an eccentricpath.

BACKGROUND OF THE INVENTION

Centripetal force results when a mass is rotated about an axis, at adistance from the axis. The centripetal force acts to counter thetendency of the mass to move in straight line, resulting in the massfollowing the curve around the axis of rotation. Understandingcentripetal force is critical to many scientific and engineeringendeavors. While centripetal force is relatively simple to understandwhen considering a perfectly circular path of rotation, the effects ofimbalance are not as intuitively understood.

One example of an imbalance system is an eccentric cam commonly used inmobile communication devices to create vibration. The eccentric cam ismounted on the spindle of a small electric motor. To create vibration,the motor is actuated and the cam is rotated about the spindle. Due tothere being more mass on one side of the cam, there is an imbalance incentripetal force as the cam rotates about the motor's spindle,resulting in vibration. The vibration results from the force imbalancecreated by the rotation. The magnitude of the force in a rotating systemis dependent on both the mass being rotated, as well as the angularvelocity. Of course, the eccentricity producing the imbalance isconstantly circulating about the motor to create the vibration and thelonger lobe of the cam created more centripetal force than the opposingside.

Studying the effect of centripetal force is typically limited toeccentric rotating masses like an eccentric cam, or the classic “figureskater” effect in which masses are pulled in or extended relative to anaxis of rotation to see the effect on angular velocity and theconservation of angular momentum. However few devices or systems areavailable to demonstrate the effect of a fixed eccentric rotation path,where the eccentricity is fixed relative to the center of rotation,while the rotating portion rotates and changes length according to itsposition of rotation. This creates a fixed centripetal forcedifferential that is useful for demonstrating various physicalphenomena, including the laws of motion, energy, and thermodynamics.

Therefore, a need exists to overcome the problems with the prior art asdiscussed above.

SUMMARY OF THE INVENTION

In accordance with some embodiments of the inventive disclosure, thereis provided a system for creating a centripetal force differential. Thesystem includes a turntable defining a plane and having a center,wherein the turntable rotates about the center such than an axis ofrotation passing through the center is normal to the plane defined bythe turntable. The system further includes a plurality of spoke elementsarranged on the turntable radially and symmetrically around the axis ofrotation, each one of the plurality of spoke elements having a fixed endadjacent the center of the turntable and a free end opposite the fixedend, wherein the free end is moveable between a minimum radial distanceand a maximum radial distance. A region around the turntable is definedinto a minimum radial distance region where the free end of each one ofthe plurality of spoke elements is controlled to be at the minimumradial distance as the spoke element passes through the minimum radialdistance region. The region also includes a maximum radial distanceregion that is opposite the minimum radial distance region relative tothe center of the turntable and where the free end of each one of theplurality of spoke elements is controlled to be at the maximum radialdistance as the spoke element passes through the maximum radial distanceregion. The region further includes a first transition region betweenminimum radial distance region and the maximum radial distance region ona first side where the free end of each one of the plurality of spokeelements is controlled to be transition from the minimum radial distanceto the maximum radial distance as the spoke element passes through thefirst transition region. The region also includes a second transitionregion between the minimum radial distance region and the maximum radialdistance region on a second side where the free end of each one of theplurality of spoke elements is from the maximum radial distance to theminimum radial distance as the spoke element passes through the firsttransition region and immediately after passing through the maximumradial distance region. The system further includes a motor connected tothe turntable on the axis of rotation that is configured to rotate theturntable and the plurality of spoke elements, wherein each spokeelement is operable to adjust its length as it rotates through theminimum radial distance region, first transition region, maximum radialdistance region, and second transition region with each rotation of theturntable.

In accordance with a further feature,

In accordance with a further feature, the system further includes aplurality of magnetic elements disposed on a frame about the minimumradial distance region, maximum radial distance region, first transitionregion and second transition region. Each one of the plurality of spokeelements includes a permanent magnet at the free end, and wherein amagnetic field of the permanent magnet opposes a magnetic field of eachof the magnetic elements such that a magnetic repulsion between thepermanent magnet at the free end of each one of the plurality of spokeelements is selected to control the length of each one of the pluralityof spoke elements.

In accordance with a further feature, the magnetic elements in theminimal radial distance region and the maximum radial distance regionare permanent magnets, and the magnetic elements in the first transitionregion and the second transition region are electromagnets. The systemfurther includes a distributor that provides current pulses to each ofthe electromagnets in synchronization with the rotation of theturntable.

In accordance with a further feature, each of the plurality of spokeelements includes a linear thruster that is operated to move a free endof the spoke element as the turntable rotates.

In accordance with a further feature, the plurality of spoke elementsincludes a top set of spoke elements on a top of the turntable, and abottom set of spoke elements on a bottom of the turntable.

In accordance with a further feature, the plurality of spoke elementscomprises four pairs of opposing spoke elements.

In accordance with a further feature, each one of the plurality of spokeelements includes, at the free end, a roller that engages a frame edgeof a frame around the turntable.

In accordance with a further feature, the roller is mounted on a springcoupled to the spoke element.

In accordance with a further feature, each one of the plurality of spokeelements is a telescoping spoke element having a plurality oftelescoping sections.

In accordance with a further feature, the system further includes aframe around the turntable, the frame having an upper frame member, alower frame member, and a middle sidewall section between the upper andlower frame members, the turntable being mounted between the upper andlower frame members.

In accordance with some embodiments of the inventive disclosure, thereis provided an apparatus for creating a relative centripetal forcedifferential that includes a turntable that rotates in a plane about acenter of the turntable and a plurality of spoke elements mounted on theturntable. The plurality of spoke elements being arranged in opposingpairs about the center of the turntable, each one of the plurality ofspoke elements having a fixed end adjacent the center of the turntableand a free end opposite the fixed end along a radial line from thecenter of the turntable, and wherein the free end is moveable relativeto the fixed end along the radial line between at least a minimumdistance and a maximum distance. The apparatus also includes a motorcoupled to the turntable to rotate the turntable. As the turntable isrotated, a length of each one of the plurality of spoke elements iscontrolled to be at the minimum distance while passing through a minimumdistance region about the turntable, wherein the minimum distance regionis defined over approximately one hundred and eighty degrees of arotation of the turntable in a region about the turntable. The length isfurther controlled to be at the maximum distance while passing through amaximum distance region that is directly opposite the minimum distanceregion and which is defined over about sixty degrees of rotation. Thelength is further controlled to be increasing from the minimum distanceto the maximum distance through a first transition region defined overabout sixty degrees of rotation between the minimum distance region andthe maximum distance region on a first side of the turntable. The lengthis further controlled to be decreasing from the maximum distance to theminimum distance through a second transition region defined over aboutsixty degrees of rotation between the maximum distance region and theminimum distance region on a second side of the turntable.

In accordance with a further feature, the apparatus further includes aplurality of magnetic elements disposed on a frame about the minimumdistance region, maximum distance region, first transition region andsecond transition region. The apparatus also includes each one of theplurality of spoke elements having a permanent magnet at the free end,and wherein a magnetic field of the permanent magnet opposes a magneticfield of each of the magnetic elements such that a magnetic repulsionbetween the permanent magnet at the free end of each one of theplurality of spoke elements is selected to control the length of eachone of the plurality of spoke elements.

In accordance with a further feature, the magnetic elements in theminimal distance region and the maximum distance region are permanentmagnets, and the magnetic elements in the first transition region andthe second transition region are electromagnets. The apparatus furtherincluding a distributor that provides current pulses to each of theelectromagnets in synchronization with the rotation of the turntable.

In accordance with a further feature, each of the spoke elements includea linear thruster that is operated to move a free end of the spokeelement as the turntable rotates.

In accordance with a further feature, the plurality of spoke elementsincludes a top set of spoke elements on a top of the turntable, and abottom set of spoke elements on a bottom of the turntable.

In accordance with a further feature, the plurality of spoke elementscomprises four pairs of opposing spoke elements.

In accordance with a further feature, each one of the plurality of spokeelements includes, at the free end, a roller that engages a frame edgeof a frame around the turntable.

In accordance with a further feature, the roller is mounted on a springcoupled to the spoke element.

In accordance with a further feature, each one of the plurality of spokeelements is a telescoping spoke element having a plurality oftelescoping sections.

In accordance with some embodiments of the inventive disclosure, thereis provided a method of creating a centripetal force differential thatincludes providing a turntable that is able to rotate about a center, aplurality of spoke elements mounted on the turntable that are arrangedin opposing pairs about the center. Each one of the plurality of spokeelements being telescoping and having a fixed end mounted on theturntable adjacent the center, and a free end opposite the fixed endalong a radial line from the center and moveable between a minimumdistance and a maximum distance. The method further includes defining,around the turntable, a plurality of regions of rotation about thecenter, including a minimum distance region defined over approximatelyone hundred eighty degrees around the center, a maximum distance regiondirectly opposite the minimum distance region and defined overapproximately sixty degrees about the center, a first transition regiondefined over approximately sixty degrees between the minimum distanceregion and the maximum distance region on a first side of the minimumand maximum distance regions, and a second transition region definedover approximately sixty degrees between the maximum distance region andthe minimum distance region on a second side of the minimum and maximumdistance regions. The method further includes rotating the turntable,and while rotating the turntable, controlling each one of the pluralityof spoke elements such the free end of each one of the plurality ofspoke elements is at the minimum distance as the spoke element rotatesthrough the minimum distance region, increased from the minimum distanceto the maximum distance as the spoke element rotates through the firsttransition region, at the maximum distance as the spoke element rotatesthrough the maximum distance region, and decreased from the maximumdistance to the minimum distance as the spoke element rotates throughthe second transition region.

Although the invention is illustrated and described herein as embodiedin a system, apparatus, and method for producing a differentialcentripetal force, it is, nevertheless, not intended to be limited tothe details shown because various modifications and structural changesmay be made therein without departing from the spirit of the inventionand within the scope and range of equivalents of the claims.Additionally, well-known elements of exemplary embodiments of theinvention will not be described in detail or will be omitted so as notto obscure the relevant details of the invention.

Other features that are considered as characteristic for the inventionare set forth in the appended claims. As required, detailed embodimentsof the present invention are disclosed herein; however, it is to beunderstood that the disclosed embodiments are merely exemplary of theinvention, which can be embodied in various forms. Therefore, specificstructural and functional details disclosed herein are not to beinterpreted as limiting, but merely as a basis for the claims and as arepresentative basis for teaching one of ordinary skill in the art tovariously employ the present invention in virtually any appropriatelydetailed structure. Further, the terms and phrases used herein are notintended to be limiting; but rather, to provide an understandabledescription of the invention. While the specification concludes withclaims defining the features of the invention that are regarded asnovel, it is believed that the invention will be better understood froma consideration of the following description in conjunction with thedrawing figures, in which like reference numerals are carried forward.The figures of the drawings are not drawn to scale.

Before the present invention is disclosed and described, it is to beunderstood that the terminology used herein is for the purpose ofdescribing particular embodiments only and is not intended to belimiting. The terms “a” or “an,” as used herein, are defined as one ormore than one. The term “plurality,” as used herein, is defined as twoor more than two. The term “another,” as used herein, is defined as atleast a second or more. The terms “including” and/or “having,” as usedherein, are defined as comprising (i.e., open language). The term“coupled,” as used herein, is defined as connected, although notnecessarily directly, and not necessarily mechanically. The term“providing” is defined herein in its broadest sense, e.g.,bringing/coming into physical existence, making available, and/orsupplying to someone or something, in whole or in multiple parts at onceor over a period of time.

“In the description of the embodiments of the present invention, unlessotherwise specified, azimuth or positional relationships indicated byterms such as “up”, “down”, “left”, “right”, “inside”, “outside”,“front”, “back”, “head”, “tail” and so on, are azimuth or positionalrelationships based on the drawings, which are only to facilitatedescription of the embodiments of the present invention and simplify thedescription, but not to indicate or imply that the devices or componentsmust have a specific azimuth, or be constructed or operated in thespecific azimuth, which thus cannot be understood as a limitation to theembodiments of the present invention. Furthermore, terms such as“first”, “second”, “third” and so on are only used for descriptivepurposes, and cannot be construed as indicating or implying relativeimportance.

In the description of the embodiments of the present invention, itshould be noted that, unless otherwise clearly defined and limited,terms such as “installed”, “coupled”, “connected” should be broadlyinterpreted, for example, it may be fixedly connected, or may bedetachably connected, or integrally connected; it may be mechanicallyconnected, or may be electrically connected; it may be directlyconnected, or may be indirectly connected via an intermediate medium. Asused herein, the terms “about” or “approximately” apply to all numericvalues, whether or not explicitly indicated. These terms generally referto a range of numbers that one of skill in the art would considerequivalent to the recited values (i.e., having the same function orresult). In many instances these terms may include numbers that arerounded to the nearest significant figure. In this document, the term“longitudinal” should be understood to mean in a direction correspondingto an elongated direction of the spoke elements. Those skilled in theart can understand the specific meanings of the above-mentioned terms inthe embodiments of the present invention according to the specificcircumstances.

BRIEF DESCRIPTION OF THE DRAWINGS

The accompanying figures, where like reference numerals refer toidentical or functionally similar elements throughout the separate viewsand which together with the detailed description below are incorporatedin and form part of the specification, serve to further illustratevarious embodiments and explain various principles and advantages all inaccordance with the present invention.

FIG. 1 is an overhead plan view of a device for generating centripetalforces, in accordance with the prior art;

FIG. 2 is an overhead plan view of a device for generating differentialcentripetal forces, in accordance with some embodiments;

FIG. 3 is a diagram of an eccentric path about an axis of rotationfollowed by masses being rotated about the axis, in accordance with someembodiments;

FIG. 4 is a chart of the force experienced by masses being rotatedaround an eccentric path, in accordance with some embodiments;

FIG. 5 is an overhead plan view of a device for generating differentialcentripetal forces, in accordance with some embodiments;

FIG. 6 is a first side cut-away view of a device for generatingdifferential centripetal forces, in accordance with some embodiments;

FIG. 7 is a second side cut-away view of a device for generatingdifferential centripetal forces, in accordance with some embodiments;

FIG. 8 shows a distributor for selectively energizing electromagnets inconjunction with the movement of masses along the eccentric path forcountering the centripetal force, in accordance with some embodiments;

FIG. 9 shows an example of peak differential between opposing spokemembers, in accordance with some embodiments;

FIG. 10 shows a plurality of telescoping spoke elements arranged inopposing pairs relative to an axis of rotation, in accordance with someembodiments;

FIG. 11 shows an overhead plan view of a centripetal force differentialsystem using spoke elements that control their own length, in accordancewith some embodiments; and

FIGS. 12A and 12B show a linear thruster in minimum and maximumextension states for use as spoke elements, in accordance with someembodiments.

DETAILED DESCRIPTION

While the specification concludes with claims defining the features ofthe invention that are regarded as novel, it is believed that theinvention will be better understood from a consideration of thefollowing description in conjunction with the drawing figures, in whichlike reference numerals are carried forward. It is to be understood thatthe disclosed embodiments are merely exemplary of the invention, whichcan be embodied in various forms.

FIG. 1 is an overhead plan view of a prior art device 100 for generatingcentripetal forces, in accordance with the prior art. The device 100includes several spoke elements 102 that extend radially from an axis ofrotation 112. At the end of each spoke element is a mass 104. The spokeelements 102 all have the same fixed length, and the mass of each of themasses 104 are identical and they have the same dimensions. Accordingly,the centripetal force acting on each mass 104 is identical. The spokeelements 102 are rotated about the axis 112, as indicated by arrow 110,each mass 104 results in a centripetal force radially outward from theaxis 112, as indicated by arrow 106 for a given point in time. The forceis countered by the spoke elements 102 holding each mass 104, and as aresult, each mass 104 follows a circular orbit around the axis 112,rather than continuing in a straight line, as would happen if, forexample, a mass 104 detached from its respective spoke element 102. Wheneach mass 104 has the same magnitude, and are each located the samedistance from the axis 112, the centripetal force of once mass acting atthe axis 112 is essentially cancelled by an opposing spoke element 102and mass 104. However, if one of the masses is made heavier, or lighter,than its opposing mass element, then an imbalance will occur duringrotation of the device. Likewise, if one spoke element is made longer,or shorter, than its opposing spoke element, than an imbalance in forceswill occur upon commencing rotation. If there is an imbalance, the netforce will be off center (i.e. not on axis 112), and the device will bepulled in the direction of the imbalanced element during rotation, whichcan produce vibration.

FIG. 2 is an overhead plan view of a device 200 for generating adifferential centripetal force, in accordance with some embodiments.Specifically, the device 200 produces a force offset that is in a fixedlocation relative to the axis of rotation, and that is independent ofthe rotating elements. A turntable 202 is generally round, and defines aplane, which, as shown in this drawing would be parallel with the planeof the drawing sheet. The turntable 202 has a center through which anaxis of rotation 204 passes perpendicularly to the plane of theturntable 202. A drive shaft is coupled to the turntable 202 along theaxis 204 so that turning the drive shaft causes the turntable 202 toturn in correspondence with the drive shaft. Mounted on the turntable202 are a plurality of telescoping spoke elements 206. The spokeelements 206 each have a first end located near the axis of rotation,and an elongated body aligned radially on the turntable 202 with respectto the axis of rotation. As shown here there are four pairs of opposingspoke elements 206.

Each one of the spoke elements 206 are telescoping, meaning that theyhave a base portion 207 mounted and fixed to the turntable 202, and atleast one moveable portion that moves relative to the base portion alonga radial line extending outward from the axis of rotation 204. As shownhere, each spoke element 206 has a base portion 207, an intermediatetelescoping section 209, and a distal telescoping section 211 that has amass 208 at a distal end that is furthest from the axis of rotation 204.The intermediate and distal sections 209, 211 slide or otherwise moverelative to each other and the base section 207, and nest into eachother. A roller and track arrangement can be used such that, forexample, intermediate section 209 is mounted on rollers that roll on atrack on the inside of base section 207, and the distal section 211 canhave a similar interconnection with the intermediate section 209.Accordingly, when the turntable 202 rotates, the telescoping sections(e.g. 209, 211) will be urged outward in response to centripetal force.The end of the distal section 211 includes a mass 208 comprised of apermanent magnet that further increases the effect of centripetal force.

Surrounding the turntable 202 in an eccentric shape and mounted on aframe around the turntable 202 are a plurality of magnetic elementsincluding permanent magnets 210 and electromagnets 212. The eccentricshape includes a semicircle around the turntable on one side at aconstant radius relative to the axis of rotation 204, On the other sideof the turntable the magnetic elements follow a non-circular path,having an arcuate portion at a greater distance from the axis ofrotation 204 and transition sections. The magnetic elements are arrangeto have an opposing polarity to the permanent magnets 208 on the distalends of each of the telescoping spoke elements 206. The magnetic force(repulsion) of the magnetic elements is selected to equal, and cancelthe centripetal force acting on the permanent magnets 208 at a selectedangular velocity of the turntable 202. Thus, as the turntable 202rotates, centripetal force urges the permanent magnets 208 on each spokeelement outward, away from the axis of rotation 204. The magneticrepulsive force created between the permanent magnets 208 and themagnetic elements 210, 212 as the permanent magnets 208 pass by themagnetic elements 210, 212 opposes and cancels the effect of thecentripetal force acting on the permanent magnet 208. Where the magneticelements 210, 212 are farther from the axis of rotation, the telescopingarrangement of the spoke elements 206 allow the permanent magnets toextend farther from the axis of rotation 204. Since all the permanentmagnets 208 are moving at the same angular velocity, those that arefarther away from the axis of rotation experience great centripetalforce and as a result exert more force on the magnetic elements 210, 212as the permanent magnets 208 pass by. Thus, is the specific arrangementshown in FIG. 2, assuming the turntable were in motion and turning,permanent magnet 214 is subject to more centripetal force than permanentmagnet 216 which is opposite the axis of rotation 204 and traveling at ashorter distance from the axis of rotation 204. Accordingly, more forceis exerted on the magnetic element proximate to permanent magnet 214that to the magnetic element proximate to permanent magnet 216, if themagnetic elements are configured to fully repel the passing permanentmagnets 208. The magnetic elements 210, 212 are configured or selectedto control the extension of the free end of the spoke elements as theypass by the magnetic elements 210, 212.

Of the magnetic elements 210, 212, the permanent magnets 210 areselected to have a magnetic field strength sufficient to oppose thecentripetal force exerted on the permanent magnets 208, and are used onthe regions having a substantially constant radius from the axis ofrotation 204. Electromagnets 212 are used in the transition regionswhere the radius to the axis of rotation 204 changes along the region.The electromagnets 212 are turned on as each permanent magnet 208approaches and passes to produce a repulsive magnetic field that canvary with the angular velocity of the turntable 204. The magneticelements 210, 212 are oriented to face the axis of rotation, although atthe start of a decreasing radius transition zone the a magnetic elementcan be angled slightly away from the axis of rotation 204.

FIG. 3 is a diagram of an eccentric path 300 about an axis of rotation(e.g. 204) followed by masses being rotated about the axis, as in FIG.2, in accordance with some embodiments. The path is mapped over avertical axis 301 and a horizontal axis 304 that is perpendicular to thevertical axis 301. The axes 301, 304 produce four quadrants including afirst quadrant 307, a second quadrant 308, a third quadrant 306, and afourth quadrant 305. The path 300 follows a semicircle 302 in the thirdand fourth quadrants 306, 305, having a radius 318 from the center 303where the axes 301, 304 meet, representing the axis of rotation (e.g.204). Thus, the semicircle 302 is the same distance away from the center303 everywhere in the third and fourth quadrants 306, 305, and is aminimum radial distance region, or simply a minimum distance region. Inthe minimum distance region of the semicircle 302 the spoke elements arein a minimum distance configuration, meaning their free end is fullywithdrawn with respect to the center 303 of rotation (e.g. the center ofthe turntable). The minimum distance region is defined over about onehundred eighty degrees of rotation, +/−3%.

In the first quadrant 307, the path follows a first transition region orfirst transition section 310 where, assuming a counter-clockwisedirection of travel about the center 303, the radius from the centerincreases to an arcuate section 312 that can have a radius that isgreater than that of the semicircle 302. In the first transition region310 the free end of each spoke element is controlled to extend,increasing the length from the minimum distance to the maximum distance.The maximum distance region 312 directly opposes the minimum distanceregion of the semicircle 302. In the maximum distance region 312 thespoke elements are controlled to have their free end at a maximumdistance from the center 303. That is, the free end of the spokeelements as they rotate through the maximum distance region is constantand at the maximum extension or distance. The first transition section310 is on a first side of the maximum and minimum distance regions (e.g.312 and 302) and extends through a portion of the first quadrant 307,such as approximately sixty degrees from the horizontal axis 304. Themaximum distance region 312 can have a constant radius along its lengthfrom about thirty degrees on either side of the vertical axis 301, orabout 60 degrees of rotation. In some embodiments the maximum distanceregion 312 can have varying distance from the center 303 with a peakradius from the center 303 at the top 316. A second transition section314 is on a second side of the maximum and minimum distance regions. Inthe second transition region 314 the free end of the spoke elements iscontrolled to decrease from the maximum distance to the minimumdistance. The second transition region 314 can be defined over aboutsixty degrees of rotation about the center 303. Accordingly, as thepermanent magnets 208 are rotated, they experience different magnitudesof centripetal force depending on where they are located relative to thecenter 303 (e.g. their distance), and the centripetal force isproportional to the their distance from the center 303 and the rotationvelocity. When the magnetic elements 210, 212 are provided along theeccentric rotation path, the force is transferred to those magneticelements 210, 212. As can be seen here, the rotation path is symmetricabout the “y” axis 316, and asymmetric about the “x” axis 304, resultingin an eccentric rotation path for the free ends of the spoke elements.While the turntable is rotated, the various regions are defined in fixedpositions about the center 303.

FIG. 4 is a chart 400 of the force experienced by masses being rotatedaround an eccentric path, in accordance with some embodiments. Inparticular, the path can be that shown in FIGS. 2 & 3. The chart 400shows a horizontal axis 402 and a vertical axis 404. The horizontal axisindicates the angle of rotation, while the vertical axis 404 indicatesthe relative magnitude of the force created by rotation. The chart hasfour quadrants corresponding to the four quadrants of FIG. 3. Thus, inthe third and fourth quadrants, along the semicircle, because the radiusis constant, the force acting on a mass being rotated along thesemicircle is constant, as indicated by line 408. The magnitude of theforce is represented by the distance from the horizontal axis 402. Theside (above or below) the horizontal axis 402 does not matter as allcentripetal force is radial. The chart 400 separates the force in thefirst and second quadrants (above the horizontal axis 402) from that ofthe third and fourth quadrants (below the horizontal axis 402). In thefirst and second quadrants, the centripetal force experienced by a massrotating along the path 300 is represented by line 410, which variesbecause the radial distance of the mass (e.g. permanent magnet 208) fromthe center of rotation varies through these quadrants, and has a peak412 at about ninety degrees, represented by the vertical line 406. Ascan be seen, a force differential is created. The effect is not unlikethat created by an eccentric cam rotating about an axis, with theexception that the eccentricity is fixed relative to the surroundingenvironment, and the mass being rotated moves along an eccentric path.The force resulting from the centripetal action is transferred to themagnetic elements 210, 212 that are fixed on a structure surrounding thepath and turntable, and on which the turntable 202 is mounted. The forceresulting from the permanent magnets 208 being rotated along theeccentric path can be measured at each of the magnetic elements 210,212, using, for example a strain gauge, to demonstrate the differentforce exerted at the various locations around the eccentric path.

In the embodiment of FIG. 2, there are shown eight spoke elements 206arrange in four opposing pairs. FIG. 9 shows an example of one opposingpair of spoke elements 206. A first spoke element 900 is shown in anextended configuration, and opposite a second spoke element 902 in acollapsed configuration. The first spoke element 900 can be, forexample, at the +90° position (e.g. 316 of FIG. 3) of the eccentricpath, and the second spoke element would therefore be in the −90°position (e.g. 318 of FIG. 3) of the eccentric path. The first spokeelement 900 includes a base section 906, and intermediate telescopingsection 908, and a distal telescoping section 910. At the distal end ofthe distal telescoping section 910 is a permanent magnet 912. Likewise,the second spoke element 902 includes a base section 914, in which theintermediate section is fully collapsed (and not shown) into the basesection 914, and the distal section 916 is mostly, if not fullycollapsed into the base section 914. The distal section 916 is partiallyshown here only to indicate it exists, and not to show a definiteposition of the section as it would be in actual operation. At thedistal end of the distal section 916 is a permanent magnet 918. Thefirst spoke element 900 is arranged in opposition to the second spokeelement 902 about an axis of rotation 904. Both of the spoke elements900, 902 are arranged along opposing radial lines extending outward fromthe axis of rotation 904. The rotation about the axis of rotation 904occur in the plane of the drawing, and at an angular velocity co. Giventhe positions of the spoke elements 900, 902 relative to the eccentricpath, the first spoke element 900 is extended fully and places thepermanent magnet 912 at a distance 920 from the axis of rotation 904.The second spoke element 902 is collapsed fully and places the permanentmagnet 918 at a distance 922 from the axis of rotation 904, wheredistance 920 is significantly greater than distance 922. Since bothpermanent magnets 912, 918 are moving at the same angular velocity, andassuming permanent magnets 912, 918 have the same mass, the first 924acting on permanent magnet 912 will be greater than the force 926 actingon permanent magnet 918 during rotation. As a result, the net force fromthe perspective of the axis of rotation 904 will be in the direction ofthe first spoke element 900.

FIG. 10 show an arrangement of eight spoke elements arranged in opposingpairs, which could be projected onto the eccentric path of FIG. 3. Thus,the spoke element at position 1002 on radial line 1008 opposes the spokeelement at position 1004 along radial line 1006. The spoke element atposition 1010 on radial line 1014 opposes the spoke element at position1012 along radial line 1016. The spoke element at position 1018 onradial line 1022 opposes the spoke element at position 1020 along radialline 1024. The spoke element at position 1026 on radial line 1030opposes the spoke element at position 1028 along radial line 1032. Eachof the spoke elements are telescoping spoke elements having a permanentmagnet 208 at their distal end, and all of the permanent magnets havesubstantially the same mass. The spoke elements at positions 1004, 1012,1020, 1026, and 1028 are all in their fully collapsed (shortest)configuration. Assuming the view shown in FIG. 10 is a moment duringrotation of the spoke elements about the axis of rotation 1034, all ofthe permanent magnets 208 will experience centripetal force that resultsin the permanent magnets following the eccentric path. The vector of theforce acting on each permanent magnet changes as it move in directionand magnitude. In the prior art arrangement of FIG. 1, the force isprovided by the arms of the spokes pulling against the 102 the mass 104.

In the inventive arrangement of FIG. 2, as illustration also here inFIG. 10, the force is provided by magnetic repulsion between thepermanent magnetic masses on the spoke elements and the magneticelements positioned around the eccentric path. The apparatus of FIG. 2demonstrates, within the appropriate reference frame, how a net forceimbalance occurs over an eccentric path of rotation. For example, atpositions 1026 and 1028, the opposing spoke elements are fullycollapsed, or otherwise in a configuration such that the masses at theends of the spoke elements are equidistant from the axis of rotation1034. As a result, the forces acting on the masses (i.e. the permanentmagnets) at these positions are equal, and opposite, cancelling eachother out. At positions 1010 and 1012, and likewise at positions 1018and 1020, the masses at positions 1010 and 1018 are located farther fromthe axis of rotation 1034 than are their opposing masses at positions1012 and 1020. As a result, there will be greater force acting on themasses at positions 1010 and 1018 than there are on those masses atpositions 1012 and 1020. Although these forces will be directed alongthe respective radial lines 1014, 1022, and 1016, 1024, these forces canbe decomposed into components along perpendicular axes through the axisof rotation 1034, with a “y” axis running through positions 1002 and1004 and the perpendicular “x” running through positions 1026 and 1028.Since the forces at positions 1010, 1018 are greater than those atpositions 1012, 1020, there is a net force along the “y” axis. The sameis true of the masses at positions 1002 and 1004, except these masseshave no force component in the “x” axis at the moment that are atpositions 1002, 1004, there is only a net force along the “y” axis. Asthe spoke elements are rotated, following the eccentric path, there willalways be a force differential relative to the axis of rotation 1034with a net force offset that is located along the “y” axis. These forcescan measured, for example, at each of the magnetic elements 210, 212 andcompared to demonstrate the effect of rotating opposing masses along aneccentric or offset path relative to the axis of rotation. This assumes,of course, that the magnetic elements 210, 212 are fixed in positionrelative to the axis of rotation, and the turntable 202. That means thestructure holding the turntable 202 is fixed to the structure holdingthe magnetic elements. As described herein, the “net force” is withrespect to the masses being rotated. Of course, other reactive forcesoccur in the overall system.

FIG. 5 is an overhead plan view of an apparatus 500 for generatingdifferential centripetal forces, in accordance with some embodiments.The apparatus is substantially similar to, and can be the same as thatshown in FIG. 2 with additional features being shown here. FIG. 6 showsa side cut-away view of the apparatus 500 taken along line A-A, and FIG.7 shows a side-cut-away view of the apparatus 500 taken along line B-B.As can be seen in FIGS. 6-7 the apparatus 500 includes upper and lowerelements in a stacked relationship. That is, for example, where in FIG.5 there is a spoke element 206 shown, as can be seen upper and loweridentical elements in a mirror image relationship.

At the distal end of the distal section, in addition to the permanentmagnet 208, there is a roller 502 that bears against a wall 506 or trackaround the eccentric path. The roller 502 is mounted on a linear bearing503 that slides against another linear bearing mounted in the distalsection 211 of the spoke element 206. The roller 502 and linear bearing503 are coupled to a spring 504 that is mounted to a fixed bracket 505on the intermediate section 209. The roller 502 and spring 504 mitigatevibration as the permanent magnet 208 of the spoke element 206 passes bythe discrete magnetic elements 210, 212 during rotation. The shape ofthe permanent magnets 208 along the outer face (facing outward from theaxis of rotation 204) is convex or arcuate to further mitigate vibrationand allow clearance in the transition sections (e.g. 310, 314) of theeccentric path. The rollers 502 can also assist in directing thepermanent magnets if the magnetic elements 210, 212 fail, or if theangular velocity of the turntable 202 is not in an optimum range.Further, it can be seen that there are wires 508 to power/activate theelectromagnets 212.

In FIGS. 6-7 two side cut-away views are shown. FIG. 6 shows theapparatus 500 when viewed along line A-A, and FIG. 7 shows the apparatus500 when viewed along the line B-B. Thus in FIG. 6 the spoke elements206 are shown fully extended and one fully collapsed being at the +90°and −90° positions, respectively. There is a top set of spoke elementsand a bottom set of spoke elements that can be aligned, as shown here,or offset. In FIG. 7 both of the spoke elements 206 are shown fullycollapsed as they are at the 0° and 180° positions. A motor 602 isprovided on a mount 603 and drives a driveshaft 604 having an axis thatdefines the axis of rotation 204. The driveshaft 604 is coupled to theturntable 202, directly or indirectly, to rotate the turntable and thespoke elements, accordingly. The mount 603 is mounted on an upper framemember 606 that can cover the top of the apparatus 500 and forms anupper structural portion. Around an outside periphery of the upper framemember 606 an upper sidewall section 616 is attached, such as withbolts. The upper sidewall section is mounted on top of a middle sidewallsection 618 in which the magnetic elements 210, 212 are disposed. Themiddle sidewall section 618 is in turn mounted on top of a lowersidewall section 614, which is mounted on a lower frame member 608 whichextends horizontally across a bottom of the apparatus 500 and can befurther mounted onto a fixture.

The turntable 202 is coupled to the fixed sections 207 of each spokeelement 206. The turntable 202 divides the upper portion from the lowerportion of the apparatus 500. Both the upper portion above the turntable202 and the lower portion below the turntable 202 have a plurality ofspoke elements 206 that have a permanent magnet 208 on their distalends, and a plurality of magnetic elements 210, 212 arranged around aneccentric path around the axis of rotation 204. In the present example,the spoke elements in the upper and lower portions are identical innumber, correspond (vertically) in location, and have the samedimensions. Accordingly, the spoke elements 206 of the upper and lowerportions are arranges in a mirror image configuration, with respect toeach, other above and below the turntable 202. The middle sidewallsection 616 holds upper and lower sets of magnetic elements 210, 212which are arranged to be at the same height as the permanent magnets 208of the respective upper and lower spoke elements 206. The rollers 502rest against the inner vertical wall of the upper and lower sidewallsections 616, 614, respectively.

The fixed sections 207 of the spoke elements 206, in addition to beingcoupled to the turntable 202, are also coupled on their opposite side toa bearing interface member; the spoke elements 206 in the upper portionare coupled to an upper bearing interface member 622, and the spokeelements 206 in the lower portion are coupled to a lower bearinginterface member 626. The upper bearing interface member 622 is furthercoupled to an upper turntable bearing 610 which is coupled to the upperframe member 606. The drive shaft 604 passes through the center of theupper turntable bearing 610. Likewise, the lower bearing interfacemember 626 is further coupled to a lower turntable bearing 612, whichfurther coupled to the lower frame member 608. The upper and lowerturntable bearings 610, 612 have two portions that rotate with respectto each other, and a roller bearing interface between those twoportions, as is well known.

The drive shaft 604 extends through the turntable assembly, through thelower turntable bearing 612, to a distributor 620, to turn an electrodeelement the distributes current to each of the electromagnets 212 inturn. Thus, there is an electrode for each set (upper and lower) ofspoke elements 206 that turns with the spoke elements and makes contactwith each of a series of electrode, in series, each of which areconnected to one of the electromagnets 212. FIG. 8 shows a distributor620 for selectively energizing electromagnets 212 in conjunction withthe movement of masses along the eccentric path for countering thecentripetal force of those masses, in accordance with some embodiments.In the view 800, the distributor 620 is shown removed from under theturntable 202 in order to show the distributor 620 more clearly. Asthere are eight spoke elements 206, the electrode 800 has eight arms,each one corresponding to one of the spoke elements 206 (or upper andlower spoke element pair). Around the electrode 800 are two contact sets801A and 801B having individual contact wipers, each corresponding toone of the electromagnets 212 and connected to its correspondingelectromagnet by a wire in wire groups 802, 804. As each electrode armpasses by a contact wiper, the distal tip of the electrode arm makescontact with the contact wiper to momentarily complete a circuit andprovide current to the corresponding electromagnet 212.

Electromagnets 212 are used in the transition sections 310, 314 to varythe strength of the magnetic field as each of the permanent magnetmasses 208 pass by each respective electromagnet 212 as these masses 208are moving along a non-perfect tangential path as in the arcuate section312 or the semicircle 302 of the third and fourth quadrants defined inFIG. 3. That is, in regions 302 and 312 the masses 208 move mostlytangentially with respect to the permanent magnets 210 as the masses 208have a constant radius with respect to the center 204, but in thetransition sections 310, 314 the radius of the masses 208 with respectto the center 204 is changing. As a mass 208 moves toward one of theelectromagnets 212, then, a half-sinusoidal current or rectangular pulseis applied to the electromagnet 212 to create a magnetic field having aflux magnitude in time to account for the non-tangential movement of amass 208 as it has been found that a static magnetic field at thelocations of the electromagnets 212 produces more vibration in masses208 as they move past the electromagnets 212. The current pulsesprovided to each electromagnet 212 are timed to peak when a mass 208 isdirectly aligned (centered) with the electromagnet 212.

Thus, electromagnets are used in the transition sections becausepermanent magnets have a permanent magnetic field with a constant fluxmagnitude. As such, if permanent magnets were to be used on the frame inthe transition sections, the magnetic field of the frame magnets 210 andthe rotational mass magnets 208 would interact with each other. Thisinteraction would cancel the net gains due to centripetal forcedifferential between the regions above and below the x-axis created bythe different distances from the rotational axis. The magnetic fieldgenerated by the electromagnets will only be activated when therotational mass magnet is facing (or perpendicular) the electromagnetand it will be turned off once the rotating mass magnet is not facing(or perpendicular) to the electromagnet. This arrangement eliminates thecanceling forces thus generating a net gain.

FIG. 11 shows an overhead plan view of a centripetal force differentialsystem 1100 using spoke elements that control their own length, inaccordance with some embodiments. That is, rather than using magneticelements disposed on a frame around turntable 1126 at the level of thespoke elements to control their length, where the free end of the spokeelements move freely, it is contemplated that self-adjusting spokeelements, such as linear thrusters, can be equivalently employed. Herethe spoke elements 1102, 1108, 1110, 1112, 1114, 1116, 1118, and 1120are all linear thrusters which have base 1106 and a linear movingportion 1104 that moves in a straight line. The moving portion of eachspoke element 1102, 1108, 1110, 1112, 1114, 1116, 1118, and 1120 iscontrolled by a motor mounted in the base that is operable to move themoving portion between a first position (e.g. a minimum distance orminimum extension) and a second position (e.g. a maximum distance orextension). The spoke elements 1102, 1108, 1110, 1112, 1114, 1116, 1118,and 1120 are arranged such the moving portion of each one moves along aradial line that extends from the center 1122. As the turntable 1126turns (i.e. in the direction of arrow 1124), each of the spoke elements1102, 1108, 1110, 1112, 1114, 1116, 1118, and 1120 control the extensionof their respective moving portion between a minimum distance positionand a maximum distance position. As shown here, spoke elements 1112,1114, 1116, 1118, and 1120 are in the minimum distance region, so themoving portion (e.g. free end) of each of these spoke elements iswithdraw to the same minimum distance or minimum extension. Spokeelement 1102 is in the maximum distance region and is at full extension.Spoke elements 1108 and 1110 are in the first and second transitionregions, respectively. Thus, spoke element 1108 is extending its movingportion outward from the minimum distance position, when it was at theposition occupied by spoke element 1120, to the maximum distanceposition. Likewise, spoke element 1110 is withdrawing its moving portionfrom the maximum to the minimum position so that it will be at theminimum position when it arrives at the point of rotation where spokeelement 1112 is shown presently.

FIGS. 12A and 12B show a linear thruster 1200 in minimum and maximumextension states, respectively, for use as spoke elements, in accordancewith some embodiments. The linear thruster 1200 includes a base 1202that can be mounted to a structure, such as a turntable, and a movingportion 1204 having a free end 1208. The moving portion moves within thebase 1202 in a linear manner and can be on tracks or other guidestructure in the base 1202. A motor 1206 is used to impart movement tothe moving portion 1204, such as by a sprocket that engages a toothedtrack in the liner portion 1204 such that rotation of the sprocket isconverted to linear movement of the moving portion 1204. An example of alinear thruster 1200 can be those made by the ALLEN-BRADLEY company andsold under the name LDAT SERIES INTEGRATED LINEAR THRUSTER. In FIG. 12Athe linear thruster 1200 is shown in the withdrawn, or minimum distanceconfiguration, and in FIG. 12B the linear thruster 1200 is in theextended position. That is, the moving portion 1204 is fully extended,or at least at a maximum extension for a given application. A pluralityof linear thrusters 1200 can be arranged as spoke elements as shown inFIG. 11, and controlled to extend/withdraw the moving portions based ontheir location through a rotation so that the free end of each linearthruster follows the eccentric path of FIG. 3.

Accordingly, the use of linear thrusters can achieve a similar result tothat of using magnetic elements and permanent magnet masses on the spokeelements, as in FIG. 1. Electric linear thrust motors can replace thetelescoping spoke elements of FIG. 1 and have a dead weight at the freeend of the actuating arm. In such an arrangement the electric linearthrust motors motor can be arranged in the same way as the spokes of thesystem using magnets. The electric linear thrust motors can be computercontrolled such their free end follows an eccentric path as in themagnetic system. In such a system all the forces would be transmitted tothe rotating turn table. A ring torque motor can be used in this system,allowing for the space necessary to install a slip ring at the centeraxis of rotation. The slip ring can be used to transmit the power anddata necessary to operate the electric linear thrust motors. Theadvantages of this system are that a specially designed electric thrustmotor can be used to generate electricity while the motors are in thetransitional quadrant (i.e. the first transition region) exerting anoutward force, and consume electricity in the quadrant requiring themass to be pull toward the rotating axis (i.e. in the second transitionregion). This system would only the require the power necessary forrotation which in theory would be zero minus electrical and mechanicallosses.

Thus the disclosed system, apparatus, and method can be used to create arelative force offset that is based on differences in centripetal forceto demonstrate how such differences affect the system, and how they canbe used. The difference in centripetal force is evident and measurablein part of the system, and the educational value in the system is indemonstrating the net effect of forces.

The claims appended hereto are meant to cover all modifications andchanges within the scope and spirit of the present invention.

What is claimed is:
 1. A system for creating a centripetal forcedifferential, comprising: a turntable defining a plane and having acenter, wherein the turntable rotates about the center such than an axisof rotation passing through the center is normal to the plane defined bythe turntable; a plurality of spoke elements arranged on the turntableradially and symmetrically around the axis of rotation, each one of theplurality of spoke elements having a fixed end adjacent the center ofthe turntable and a free end opposite the fixed end, wherein the freeend is moveable between a minimum radial distance and a maximum radialdistance, wherein, a region around the turntable is defined into: aminimum radial distance region where the free end of each one of theplurality of spoke elements is controlled to be at the minimum radialdistance as the spoke element passes through the minimum radial distanceregion; a maximum radial distance region that is opposite the minimumradial distance region relative to the center of the turntable and wherethe free end of each one of the plurality of spoke elements iscontrolled to be at the maximum radial distance as the spoke elementpasses through the maximum radial distance region; a first transitionregion between minimum radial distance region and the maximum radialdistance region on a first side where the free end of each one of theplurality of spoke elements is controlled to transition from the minimumradial distance to the maximum radial distance as the spoke elementpasses through the first transition region; a second transition regionbetween the minimum radial distance region and the maximum radialdistance region on a second side where the free end of each one of theplurality of spoke elements is controlled to transition from the maximumradial distance to the minimum radial distance as the spoke elementpasses through the first transition region and immediately after passingthrough the maximum radial distance region; and a motor connected to theturntable on the axis of rotation that is configured to rotate theturntable and the plurality of spoke elements, wherein each spokeelement is operable to adjust its length as it rotates through theminimum radial distance region, first transition region, maximum radialdistance region, and second transition region with each rotation of theturntable.
 2. The system of claim 1, further comprising: a plurality ofmagnetic elements disposed on a frame about the minimum radial distanceregion, maximum radial distance region, first transition region andsecond transition region; and each one of the plurality of spokeelements includes a permanent magnet at the free end, and wherein amagnetic field of the permanent magnet opposes a magnetic field of eachof the magnetic elements such that a magnetic repulsion between thepermanent magnet at the free end of each one of the plurality of spokeelements is selected to control the length of each one of the pluralityof spoke elements.
 3. The system of claim 2, wherein: the magneticelements in the minimal radial distance region and the maximum radialdistance region are permanent magnets; and the magnetic elements in thefirst transition region and the second transition region areelectromagnets, the system further including a distributor that providescurrent pulses to each of the electromagnets in synchronization with therotation of the turntable.
 4. The system of claim 1, wherein each of theplurality of spoke elements includes a linear thruster that is operatedto move a free end of the spoke element as the turntable rotates.
 5. Thesystem of claim 1, wherein the plurality of spoke elements includes atop set of spoke elements on a top of the turntable, and a bottom set ofspoke elements on a bottom of the turntable.
 6. The system of claim 1,wherein the plurality of spoke elements comprises four pairs of opposingspoke elements.
 7. The system of claim 1, wherein each one of theplurality of spoke elements includes, at the free end, a roller thatengages a frame edge of a frame around the turntable.
 8. The system ofclaim 7, wherein the roller is mounted on a spring coupled to the spokeelement.
 9. The system of claim 1, wherein each one of the plurality ofspoke elements is a telescoping spoke element having a plurality oftelescoping sections.
 10. The system of claim 1, further comprising aframe around the turntable, the frame having an upper frame member, alower frame member, and a middle sidewall section between the upper andlower frame members, the turntable being mounted between the upper andlower frame members.
 11. An apparatus for creating a relativecentripetal force differential, comprising: a turntable that rotates ina plane about a center of the turntable, a plurality of spoke elementsmounted on the turntable, the plurality of spoke elements arranged inopposing pairs about the center of the turntable, each one of theplurality of spoke elements having a fixed end adjacent the center ofthe turntable and a free end opposite the fixed end along a radial linefrom the center of the turntable, wherein the free end is moveablerelative to the fixed end along the radial line between at least aminimum distance and a maximum distance; a motor coupled to theturntable to rotate the turntable; wherein as the turntable is rotated,a length of each one of the plurality of spoke elements is controlled tobe: at the minimum distance while passing through a minimum distanceregion about the turntable, wherein the minimum distance region isdefined over approximately one hundred and eighty degrees of a rotationof the turntable in a region about the turntable; at the maximumdistance while passing through a maximum distance region that isdirectly opposite the minimum distance region and which is defined overabout sixty degrees of rotation; increasing from the minimum distance tothe maximum distance through a first transition region defined overabout sixty degrees of rotation between the minimum distance region andthe maximum distance region on a first side of the turntable; anddecreasing from the maximum distance to the minimum distance through asecond transition region defined over about sixty degrees of rotationbetween the maximum distance region and the minimum distance region on asecond side of the turntable.
 12. The apparatus of claim 11, furthercomprising: a plurality of magnetic elements disposed on a frame aboutthe minimum distance region, maximum distance region, first transitionregion and second transition region; and each one of the plurality ofspoke elements includes a permanent magnet at the free end, and whereina magnetic field of the permanent magnet opposes a magnetic field ofeach of the magnetic elements such that a magnetic repulsion between thepermanent magnet at the free end of each one of the plurality of spokeelements is selected to control the length of each one of the pluralityof spoke elements.
 13. The apparatus of claim 12, wherein: the magneticelements in the minimal distance region and the maximum distance regionare permanent magnets; and the magnetic elements in the first transitionregion and the second transition region are electromagnets, theapparatus further including a distributor that provides current pulsesto each of the electromagnets in synchronization with the rotation ofthe turntable.
 14. The apparatus of claim 11, wherein each of the spokeelements include a linear thruster that is operated to move a free endof the spoke element as the turntable rotates.
 15. The apparatus ofclaim 11, wherein the plurality of spoke elements includes a top set ofspoke elements on a top of the turntable, and a bottom set of spokeelements on a bottom of the turntable.
 16. The apparatus of claim 11,wherein the plurality of spoke elements comprises four pairs of opposingspoke elements.
 17. The apparatus of claim 11, wherein each one of theplurality of spoke elements includes, at the free end, a roller thatengages a frame edge of a frame around the turntable.
 18. The apparatusof claim 17, wherein the roller is mounted on a spring coupled to thespoke element.
 19. The apparatus of claim 11, wherein each one of theplurality of spoke elements is a telescoping spoke element having aplurality of telescoping sections.
 20. A method of creating acentripetal force differential, comprising: providing a turntable thatis able to rotate about a center, a plurality of spoke elements mountedon the turntable that are arranged in opposing pairs about the center,each one of the plurality of spoke elements being telescoping and havinga fixed end mounted on the turntable adjacent the center, and a free endopposite the fixed end along a radial line from the center and moveablebetween a minimum distance and a maximum distance; defining around theturntable a plurality of region of rotation about the center including aminimum distance region defined over approximately one hundred eightydegrees around the center, a maximum distance region directly oppositethe minimum distance region and defined over approximately sixty degreesabout the center, a first transition region defined over approximatelysixty degrees between the minimum distance region and the maximumdistance region on a first side of the minimum and maximum distanceregions, and a second transition region defined over approximately sixtydegrees between the maximum distance region and the minimum distanceregion on a second side of the minimum and maximum distance regions;rotating the turntable; and while rotating the turntable, controllingeach one of the plurality of spoke elements such the free end of eachone of the plurality of spoke elements is: at the minimum distance asthe spoke element rotates through the minimum distance region; increasedfrom the minimum distance to the maximum distance as the spoke elementrotates through the first transition region; at the maximum distance asthe spoke element rotates through the maximum distance region; anddecreased from the maximum distance to the minimum distance as the spokeelement rotates through the second transition region.